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3 years ago

5

Domain and range of f(x)=√(2x-3)/x^2-5x+4

1 answer:

marshall27 [118]3 years ago

5 0

Answer:

<em>Domain:</em> [ 3/ 2 , ∞ ) , { x ∣ x ≥ 3 /2 }

<em>Range:</em> { x | }

Step-by-step explanation:

To find the domain, find where the function is defined. The range is just the set of values that correspond with the domain.

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I am in need of assistance.

Alex_Xolod [135]

Answer:

A. x = 6.08, x = -0.58

Step-by-step explanation:

$\displaystyle \frac{2x}{x-4}-\frac{2x-5}{x^2-10x+24}=\frac{-3}{x-6}$

1. Factor the denominator.

$\displaystyle \frac{2x}{x-4}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

2. Multiply the leftmost fraction by (x-6)/(x-6) to get common denominators.

$\displaystyle \Big ( \frac{x-6}{x-6} \Big ) \frac{2x}{x-4}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

3. Simplify.

$\displaystyle \frac{2x^2-12x}{(x-4)(x-6)}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

4. Combine like terms.

$\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3}{x-6}$

5. Multiply the right side of the equation by (x-4)/(x-4).

$\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3}{x-6} \Big ( \frac{x-4}{x-4} \Big )$

6. Simplify.

$\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3x+12}{(x-6)(x-4)}$

7. "Cancel" out the denominators because they are equivalent.

$2x^2-14x+5=-3x+12$

8. Set the equation equal to 0.

$2x^2-11x-7=0$

Quadratic formula:

$\displaystyle x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}$

9. Factor using the quadratic formula.

$\displaystyle x = \frac{-(-11)\pm \sqrt{(-11)^2-4(2)(-7)} }{2(2)}$

10. Multiply and simplify.

$\displaystyle x = \frac{11 \pm \sqrt{177} }{4}$

11. Plug this into your calculator and solve for x.

$x=6.07603367 \approx 6.08$
$x=-0.57603367 \approx -0.58$

The correct answer is A. x = 6.08, x = -0.58.

8 0

3 years ago

Find the area of a regular hexagon with an apothem 17.3 miles long and a side 20 miles long

Zinaida [17]

The area of a hexagon is $\frac{3 \sqrt{3} }{2} a^{2}$ where a = one side

$\frac{3 \sqrt{3} }{2} 20^{2}$

$\frac{3*200 \sqrt{3} }{2}$

$\frac{600 \sqrt{3} }{2}$

$300 \sqrt{3}$ ≈ 1038 mi²

4 0

3 years ago

Mrs. Grady surveyed 30 students, 12 of which said they liked basketball, 16 of which said they liked hockey, and 4 of which said

diamong [38]

Because 4 people likes both, we take out 4 from the sum of both the number to avoid double count.

People who like both sports = 12 + 16 - 4 = 24
People who do not like either sport = 30 - 24 = 6

4 0

4 years ago

A rectangle has a length of x + 5 and a

Zinaida [17]

Answer:

6x - 8

Step-by-step explanation:

$P = 2(x + 5) + 2(2x - 9)\\P = 2x + 10 + 4x - 18\\P = 6x - 8$

4 0

3 years ago

Three times b more than 100 is equal to the product of 6 and b

Anestetic [448]

3(b+100)= 6b
3b + 300 = 6b
300 = 3b
b = 100

6 0

4 years ago